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Math Problems
Grade 8
Percent of change
Zaid and Matias, two farmers, constructed a
792
792
792
-foot fence around their very large garden. If Zaid constructed
20
%
20\%
20%
more of the fence than Matias did, how many feet of the fence did Zaid construct?
\newline
□
\square
□
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John is a quarterback. This year, he completed
350
350
350
passes, which is
70
%
70\%
70%
of all the passes he's thrown this year. How many passes has John thrown this year?
\newline
◻
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Carson invested
$
2000
\$2000
$2000
in an investment account that earns
5
%
5\%
5%
interest compounded continuously. How much money will she have in her account at the end of her
8
8
8
th year of investing?
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Mrs Ang sold some cakes in January. In February, she decreased the price of each cake by
20
%
20 \%
20%
and sold
40
%
40 \%
40%
more cakes than in January. Given that she earned
$
234
\$ 234
$234
more from the sale of cakes in February than in January, how much money did she earn in February?
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In a community service class in the fall,
3
3
3
of the
15
15
15
class sessions were lectures, while all others were devoted to fieldwork in parks. In the spring, the number of sessions devoted to fieldwork remained the same, but the total number of sessions increased to
18
18
18
. In the spring, what percent of class sessions were lectures?
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The schoolyard has
12
12
12
trees. The number of maple trees is
3
3
3
less than twice the number of oak trees. How many maple trees are there in the schoolyard?
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You have inherited land that was purchased for
$
30
,
000
\$ 30,000
$30
,
000
in
1960
1960
1960
. The value of the land increased by approximately
5
%
5 \%
5%
per year. What is the approximate value of the land in the year
2011
2011
2011
?
\newline
(A)
$
15
,
000
\$ 15,000
$15
,
000
\newline
(B)
$
344
,
022
\$ 344,022
$344
,
022
\newline
(C)
$
31
,
500
\$ 31,500
$31
,
500
\newline
(D)
$
28
,
500
\$ 28,500
$28
,
500
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A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is
20
%
20 \%
20%
more than the number of shoppers the day before. The total number of shoppers over the first
4
4
4
days is
671
671
671
.
\newline
How many shoppers were at the mall on the first day?
\newline
Round your final answer to the nearest integer.
\newline
□
\square
□
shoppers
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Happy Town had a circus performance during the school holidays.
20
%
20\%
20%
of the people were performers and the rest were audience. Female performers were twice the number of male performers.
60
%
60\%
60%
of the audience were male and there were
1200
1200
1200
more male audience than female audience. After some males left the circus,
20
%
20\%
20%
of the remaining people in the circus were male. How many males left the circus?
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Lee scored
25
25
25
points in yesterday's game. That was
3
3
3
more than twice the number of points Alex scored.
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In
2013
2013
2013
, the population of Nevada and North Carolina were each growing at a rate of approximately
3.3
%
3.3\%
3.3%
per year. In addition, the US Census Bureau estimated that the population of Nevada and North Carolina was
2.8
2.8
2.8
million and
9.8
9.8
9.8
million people, respectively. If the population growth rates in each of these states remained the same, approximately how many more people were living in North Carolina compared to Nevada in
2014
2014
2014
?
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\newline
Keegan makes a deposit into her savings account at the beginning of the year. The account earns
3
%
3 \%
3%
simple interest each year. She has
$
360.50
\$ 360.50
$360.50
in her account at the end of the year. If Keegan did not make any additional deposits or withdrawals during the year, ho much did she deposit into the account at the beginning of the year?
\newline
$
10.82
\$ 10.82
$10.82
\newline
$
277.31
\$ 277.31
$277.31
\newline
$
350.00
\$ 350.00
$350.00
\newline
$
371.32
\$ 371.32
$371.32
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John is a quarterback. Till October, he completed
350
350
350
passes, and plans to add
20
%
20 \%
20%
to this number by end of the year. How many passes will John attempt this year?
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The swimming pool is open when the high temperature is higher than
20
∘
C
20 \, ^{\circ}\mathrm{C}
20
∘
C
. Lainey tried to swim on Monday and Thursday (which was days
3
3
3
later). The pool was open on Monday, but it was closed on Thursday. The high temperature was
30
∘
C
30 \, ^{\circ}\mathrm{C}
30
∘
C
on Monday, but decreased at a constant rate in the next
3
3
3
days. Write an inequality to determine the rate of temperature decrease in degrees Celsius per day,
d
d
d
, from Monday to Thursday
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In
2010
2010
2010
, the population of a city was
240
,
000
240,000
240
,
000
. From
2010
2010
2010
to
2015
2015
2015
, the population grew by
5.3
%
5.3\%
5.3%
. From
2015
2015
2015
to
2020
2020
2020
, it fell by
3.5
%
3.5\%
3.5%
. To the nearest whole number, by what percent did the city grow from
2010
2010
2010
to
2020
2020
2020
?
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Dominic bought stock in a company two years ago that was worth
x
x
x
dollars. During the first year that he owned the stock, it increased by
31
%
31\%
31%
. During the second year the value of the stock increased by
6
%
6\%
6%
. Write an expression in terms of
x
x
x
that represents the value of the stock after the two years have passed.
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In one community college, the cost per credit hour for in-state students has been increasing by
$
3
\$3
$3
a year. In another community college, it has been increasing by
9
%
9\%
9%
per year. This year, the cost is
$
65
\$65
$65
at both colleges. To the nearest dollar, what was the positive difference in costs
2
2
2
years ago?
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A tree increases its number of nuts at the rate of
100
%
100\%
100%
every year. What was the number of nuts
5
5
5
years ago, if this year it gave
3
,
200
3,200
3
,
200
nuts?
\newline
A)
500
500
500
nuts
\newline
B)
100
100
100
nuts
\newline
C)
320
320
320
nuts
\newline
D)
640
640
640
nuts
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One year, the population of a city was
364
364
364
,
000
000
000
. Several years later it was
323
323
323
,
960
960
960
.
\newline
Find the percent decrease.
\newline
Answer:__________
%
\%
%
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One year, the population of a city was
392
392
392
,
000
000
000
. Several years later it was
427
427
427
,
280
280
280
.
\newline
Find the percent increase.
\newline
Answer: ________
%
\%
%
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One year, the population of a city was
376
376
376
,
000
000
000
. Several years later it was
338
338
338
,
400
400
400
.
\newline
Find the percent decrease.
\newline
Answer:________
%
\%
%
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Marques has a loyalty card good for a discount at his local pharmacy. The item he wants to buy is priced at
$
7
\$ 7
$7
, before discount and tax. After the discount, and before tax, the price is
$
6.58
\$ 6.58
$6.58
. Find the percent discount.
\newline
Answer: _____
%
\%
%
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One year, the population of a city was
156
156
156
,
000
000
000
. Several years later it was
177
177
177
,
840
840
840
. Find the percent increase.
\newline
Answer: _____
%
\%
%
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One year, the population of a city was
391
391
391
,
000
000
000
. Several years later it was
355
355
355
,
810
810
810
. Find the percent decrease.
\newline
Answer:_____
%
\%
%
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To find the population of a city next year, we multiply its current population by
1
1
1
.
026
026
026
. By what percent does the population increase per year?
\newline
Answer:
%
\%
%
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Amira invests money in an account paying simple interest. No money is added or removed from the investment. To find the balance after a year, she multiplies her current balance by
1
1
1
.
015
015
015
. What percent simple interest does the account earn per year?
\newline
Answer: ______
%
\%
%
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Carter invests money in an account paying simple interest. No money is added or removed from the investment. To find the balance after a year, he multiplies his current balance by
1
1
1
.
014
014
014
. What percent simple interest does the account earn per year?
\newline
Answer: ______
%
\%
%
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To find the population of a city next year, we multiply its current population by
0
0
0
.
981
981
981
. By what percent does the population decrease per year?
\newline
Answer: ______
%
\%
%
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To find the population of a city next year, we multiply its current population by
1
1
1
.
024
024
024
. By what percent does the population increase per year?
\newline
Answer:______
%
\%
%
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The population of a city decreases by
2
%
2 \%
2%
per year. If this year's population is
p
p
p
, which expression represents next year's population?
\newline
0.02
p
0.02 p
0.02
p
\newline
0.98
p
0.98 p
0.98
p
\newline
0.998
p
0.998 p
0.998
p
\newline
2
p
2 p
2
p
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The population of a city decreases by
4.1
%
4.1 \%
4.1%
per year. If this year's population is
p
p
p
, which expression represents next year's population?
\newline
0
0
0
.
959
959
959
\newline
4.1
p
4.1 p
4.1
p
\newline
1
p
−
0.041
p
1 p-0.041 p
1
p
−
0.041
p
\newline
0.041
p
0.041 p
0.041
p
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The population of a city decreases by
3.9
%
3.9 \%
3.9%
per year. If this year's population is
p
p
p
, which expression represents next year's population?
\newline
0.9961
p
0.9961 p
0.9961
p
\newline
1
−
0.039
p
1-0.039 p
1
−
0.039
p
\newline
3.9
p
3.9 p
3.9
p
\newline
0.961
p
0.961 p
0.961
p
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The population of a city increases by
2.2
%
2.2 \%
2.2%
per year. If this year's population is
p
p
p
, which expression does NOT represent next year's population?
\newline
p
+
0.022
p
p+0.022 p
p
+
0.022
p
\newline
1
+
0.022
p
1+0.022 p
1
+
0.022
p
\newline
1
p
+
0.022
p
1 p+0.022 p
1
p
+
0.022
p
\newline
(
1
+
0.022
)
p
(1+0.022) p
(
1
+
0.022
)
p
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At the beginning of the week, Josh had
133
%
133\%
133%
computer games, as many computer games as Peter had. By the end of the week, Josh gave
25
%
25\%
25%
of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week?
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During one time period, the price of rhodium increased at a rate that was proportional to the price of rhodium at that time. The price for an ounce of rhodium was
475
475
475
initially, and it quadrupled every
25
25
25
months. What was the price for an ounce of rhodium after
18
18
18
months?
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During last year's basketball season, Jackson attempted
150
150
150
free throws of which he made
120
120
120
. far this season, he's attempted
24
24
24
and made
16
16
16
. A player's free-throw percentage is defined to be the percent of free-throws made out of the number of free-throws attempted. Assuming calculations began with the start of last year's season, which of the following best approximates Jackson's overall free-throw percentage to date?
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A high school's graduation rate is defined to be the percentage of the senior class that graduates. Last year
406
406
406
of Sagamore High School's
452
452
452
seniors graduated. This year the school expects the previous year's graduation rate to increase by approximately
2
2
2
percentage points. If there are
436
436
436
students in this year's senior class, which of the following best approximates the number of seniors that Sagamore High School expects to graduate this year?
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A plant was
20
cm
20\,\text{cm}
20
cm
tall last month. This month, it grew by
25
%
25\%
25%
. What is its height this month?
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A plant was
20
cm
20\,\text{cm}
20
cm
tall last month. This month, it grew by
25
%
25\%
25%
. What is its height this month?
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Emma weighed
150
150
150
pounds at the beginning of the year. She decided to lose weight and succeeded in losing
10
%
10\%
10%
of her body weight. What is her current weight?
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Finley's pumpkin had a mass of
6
6
6
.
5
5
5
kilograms
(
k
g
)
(\mathrm{kg})
(
kg
)
before he carved it. After it was carved, the pumpkin had a mass of
3.9
k
g
3.9 \mathrm{~kg}
3.9
kg
.
\newline
What was the percent decrease in the mass of the pumpkin?
\newline
_____\(\%\)
\newline
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Aubrey's dinner cost
$
85
\$ 85
$85
. She tips the waitstaff
30
%
30 \%
30%
for excellent service.
\newline
How much does Aubrey tip the waitstaff?
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John is a quarterback. This year, he completed
350
350
350
passes, which is
70
%
70\%
70%
of all the passes he's attempted this year.
\newline
How many passes has John attempted this year?
\newline
passes
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The population of Springville is on the rise. Each year, on January
1
1
1
, the town holds its own census and the population is recorded. In
2010
2010
2010
, the town recorded a population of
12
,
000
12,000
12
,
000
. The
2011
2011
2011
census reported a
5
%
5\%
5%
increase from the
2010
2010
2010
population, and the
2012
2012
2012
census reported a
7
%
7\%
7%
increase from the
2011
2011
2011
population. By how many people did the population of Springville increase over the
2
2
2
-year period?
\newline
Choose
1
1
1
answer:
\newline
(A)
240
240
240
\newline
(B)
882
882
882
\newline
(C)
1440
1440
1440
\newline
(D)
1482
1482
1482
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Haruka hiked several kilometers in the morning. She hiked only
6
6
6
kilometers in the afternoon, which was
25
%
25\%
25%
less than she had hiked in the morning. How many kilometers did Haruka hike in all?
\newline
□
\square
□
kilometers
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An author published a book which was being sold online. The first month the author sold
22100
22100
22100
books, but the sales were declining steadily at
10
%
10 \%
10%
each month. If this trend continues, how many total books would the author have sold over the first
22
22
22
months, to the nearest whole number?
\newline
Answer:
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
5660
\$ 5660
$5660
and his stock in Company B was worth
$
750
\$ 750
$750
. The stock in Company A has increased
5
%
5 \%
5%
since last year and the stock in Company B has increased
22
%
22 \%
22%
. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
\newline
Answer:
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
5740
\$ 5740
$5740
and his stock in Company B was worth
$
3250
\$ 3250
$3250
. The stock in Company A has increased
25
%
25\%
25%
since last year and the stock in Company B has increased
24
%
24 \%
24%
. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
\newline
Answer:
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
4480
\$ 4480
$4480
and his stock in Company B was worth
$
4600
\$ 4600
$4600
. The stock in Company A has increased
10
%
10\%
10%
since last year and the stock in Company B has increased
8
%
8 \%
8%
. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
\newline
Answer:
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Last year at a certain high school, there were
120
120
120
ninth graders on the honor roll and
105
105
105
tenth graders on the honor roll. This year, the number of ninth graders on the honor roll decreased by
25
%
25 \%
25%
and the number of tenth graders on the honor roll decreased by
20
%
20 \%
20%
. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).
\newline
Answer:
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